410 



LAM. SEPARATION 

 NEAR MIDCHOHD 



60'/. SLIP 

 Re^ = 0.47x10^ 



FIGURE 12. Variation of the critical radius with 

 propeller loading on propeller D (suction side) . 



calculations were made, using the pressure distri- 

 butions as calculated in Section 3. The laminar 

 boundary layer was calculated with Thwaites ' method 

 [Thwaites (1949)]. Laminar separation was predicted 

 using Curie and Skan's (1957) criteron. This cal- 

 culation method does not take into account the 

 delaying effect of rotation on laminar separation, 

 but since laminar separation occurs very close to 

 the leading edge the effect of rotation on the 

 development of the boundary layer will still be 

 small . The correlation between the calculated and 

 the observed critical radius is given in Figure 14, 

 and this correlation is quite good. The critical 

 radius at all conditions and the variation of the 

 critical radius between the propeller blades can 



CRITICAL RADIUS 



FIGURE 13. Discontinuity of paint streaks at the 

 critical radius. 



CALCULATED 



FIGURE 14. Correlation of calculated radius of 

 laminar separation and measured critical radius. 



also be found from Figure 14. As can be seen, the 

 variation of the critical radius per blade in one 

 condition can be considerable , showing the sensi- 

 tivity of laminar separation to the manufacturing 

 accuracy. The critical radius per blade, however, 

 reproduced remarkably. 



The position of laminar separation is independent 

 of the Reynolds number. So another check on the 

 hypothesis of laminar separation at the critical 

 radius is the independence of the critical radius 

 from the Reynolds number. Propellers A and C were 

 therefore tested with about twice the original 

 number of revolutions. Propeller A was also inves- 

 tigated in a cavitation tunnel : the highest 

 Reynolds number in the towing tank was repeated 

 and another condition with about three times the 

 original Reynolds number was tested. The paint 

 tests in the cavitation tunnel were less accurate 

 since turbulent spots occurred, which caused a 

 wedge shaped tangential streak through the laminar 

 pattern. This was strongest at the higher Reynolds 

 numbers. 



Figure 15 gives the critical radius as a function 

 of Reynolds number for the blades available for 

 comparison. There is a slight trend for the critical 

 radius to decrease with increasing Reynolds number, 

 but this is only very slight. The critical radius 

 is strongly dependent on the propeller loading and 

 a slight increase of the propeller loading with 

 increasing Reynolds number might cause the decrease 

 of the critical radius. For comparison the obser- 

 vations of Sasajima are also drawn in Figure 15. 

 He observes a larger shift of the critical radius 

 with Reynolds number, but his results from the 

 tank show no variation with Reynolds number. The 

 variations found in the cavitation tunnel might 

 well be caused by variations in propeller loading 

 or by wall effects. The conclusion seems justified 

 that the critical radius is independent of the 

 Reynolds number, at least until natural transition 

 occurs close to the minimum pressure point. In 

 that case a critical radius no longer exists. 



